{
  "id": "2408.02602",
  "version": "v1",
  "published": "2024-08-05T16:22:28.000Z",
  "updated": "2024-08-05T16:22:28.000Z",
  "title": "Large time effective kinetics $β$-function for quantum (2+p)-spin glass",
  "authors": [
    "Vincent Lahoche",
    "Dine Ousmane Samary",
    "Parham Radpay"
  ],
  "comment": "32 pages, 33 figures",
  "categories": [
    "cond-mat.dis-nn"
  ],
  "abstract": "This paper examines the quantum $(2+p)$-spin dynamics of a $N$-vector $\\textbf{x}\\in \\mathbb{R}^N$ through the lens of renormalization group (RG) theory. The RG is based on a coarse-graining over the eigenvalues of matrix-like disorder, viewed as an effective kinetic whose eigenvalue distribution undergoes a deterministic law in the large $N$ limit. We focus our investigation on perturbation theory and vertex expansion for effective average action, which proves more amenable than standard nonperturbative approaches due to the distinct non-local temporal and replicative structures that emerge in the effective interactions following disorder integration. Our work entails the formulation of rules to address these non-localities within the framework of perturbation theory, culminating in the derivation of one-loop $\\beta$-functions. Our explicit calculations focus on the cases $p=3$, $p=\\infty$, and additional analytic material is given in the appendix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-05T16:22:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large time effective kinetics",
      "perturbation theory",
      "eigenvalue distribution undergoes",
      "additional analytic material",
      "distinct non-local temporal"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}